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1d
asked Determine the valuation of $\rho$ with $F = k(x,\rho)$ at the only place above $(\infty)$.
Nov
12
accepted Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible
Nov
12
comment Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible
The source is part of some lecture notes from my professor and therefore I wasn't sure if I'm allowed to put that here; besides it's written in german. And yes, $P + \mathcal{F} = B$ was used to show that $B_P$ is a DVR. Again, thank you very much!
Nov
12
comment Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible
I thought about this before but I kind of scrapped that idea for no reason. Of course this is the answer, it's clear now! Thank you very much.
Nov
12
asked Prime ideal $P$ in $R$ coprime to the conductor plus the localization $R_{P}$ is a DVR implies that $P$ is invertible
Jul
31
awarded  Teacher
Jul
25
comment Why is every Divisor of the rational function field $K(x)$ over $K$ a principal divisor if $K$ is algebraically closed
So the statement is wrong as I suggested. Because the degree of a prime divisor is 1.
Jul
24
asked Why is every Divisor of the rational function field $K(x)$ over $K$ a principal divisor if $K$ is algebraically closed
Jun
5
comment What is meant by $|dxdy|^{1/2}$ in the integral?
What does the symbol $\wedge$ mean and thus $dx \wedge dy$?
Jun
5
comment What is meant by $|dxdy|^{1/2}$ in the integral?
And how would this expression change under changes of coordinates? I'm sorry if this is fundamental, but I'm not very familiar with analysis this deep. We had the projective coordinates: $x = x$ and $s = y/x$. So how would the written object change under the change of coordinates to those above?
Jun
5
asked What is meant by $|dxdy|^{1/2}$ in the integral?
Apr
16
comment Characterization of transcendental elements in algebraic function fields
@ YACP: Thank you very much for your help!
Apr
16
accepted Characterization of transcendental elements in algebraic function fields
Apr
16
comment Characterization of transcendental elements in algebraic function fields
Now I got it. If $z$ is transcendental over $K(X)$, then $K(z) \cong K(X)$ and $X$ is clearly algebraic over $K(X)$ since $X\cdot X^1 + X^2 \cdot X^0 = 0$ and $X \neq 0$ and $X^2 \neq 0$.
Apr
16
comment Characterization of transcendental elements in algebraic function fields
To the second part: Why is $z$ algebraic over $K(X)$, if $z$ is transcendental over $K$? EDIT: I haven't met him yet.
Apr
15
comment Characterization of transcendental elements in algebraic function fields
Does this change the situation to a convincing one? And yes, I'm new to field theory.
Apr
15
awarded  Editor
Apr
15
revised Characterization of transcendental elements in algebraic function fields
added 178 characters in body
Apr
15
asked Characterization of transcendental elements in algebraic function fields
Jan
22
answered Book/tutorial recommendations: acquiring math-oriented reading proficiency in German